High-dimension vectors arise when computing similarity of items that cannot be conveniently represented by a total ordering, such as numbers or alphabetic strings. This presents a problem. For example, in one approach the similarity of images can be computed using “signatures” derived from high-dimension vectors obtained from spectral techniques such as FFT and DCT [Celentano 1997 (@inproceedings{celentano97fftbased, author=“Augusto Celentano and Vincenzo Di Lecce”, title=“{FFT}-Based Technique for Image-Signature Generation”, booktitle=“Storage and Retrieval for Image and Video Databases ({SPIE})”, pages=“457-466”, year=“1997”, url=“citeseer.ist.psu.edu/597114.html”})]. Matches between short sections of music (frames) within a song or piece can be computed by the Mel-frequency cepstral coefficients (MFCC) [Logan 2001 (@misc{logan01contentbased, author=“B. Logan and A. Salomon”, title=“A content-based music similarity function”, text=“B. Logan and A. Salomon. A content-based music similarity function. Technical report, Compaq Cambridge Research Laboratory, June 2001.”, year=“2001”, url=“citeseer.ist.psu.edu/logan01contentbased.html”})], which are derived from a discrete-cosine transformation (DCT). Similarity between chromosomes stored in a genomic databank can be computed by representing the nucleotide sequences as sparse vectors of high dimension derived from a Markov transition model [Nakano 2004 (Russell Nakano, “Method and apparatus for fundamental operations on token sequences: computing similarity, extracting term values, and searching efficiently”, U.S. Patent Application, 20040162827, Aug. 19, 2004.)].